Michelson-Morley's experiment

why does the other ray in Michelson experiment has to travel a longer path?It seems to me that the other ray knows which path it has to travel.I found this myterious error at newbielink:http://users.net.yu/~mrp/chapter5.html [nonactive] .How comes the other ray moving perpendicular to the earth's motion cover a distance of 2a instead of 2L ?

I'm afraid I don't understand your confusion. I don't see an error in the calculations on that web page.

What they're trying to calculate is the distance travelled through "absolute space", i.e. outside the experimental apparatus. If the apparatus was stationary in "absolute space", then yes, the distances would be the same for both rays.

Perhaps you could think of the following analogy: Imagine you're sitting in a moving car and you throw a ball from your hand up to the ceiling of the car (say, a distance of 1 foot) and it bounces straight back down to your hand. People sitting in the car with you would see the ball travel straight up and down, a total distance of 2 feet.

But to someone standing at the side of the road, they wouldn't see the ball go straight up and down - they'd see it make the path of a triangle. If, in the time between you throwing the ball up and catching it again, the car had moved forward a distance of 2 feet, then to the person at the side of the road the ball would have travelled up the hypoteneuse of a right angle triangle and down a similar slanted path - and they'd calculate the total distance travelled by the ball to be 2.8 feet. (2 x square-root-of-2, using pythagoras' theorem.)

I'm not sure I've explained myself very well, but I hope it helps.

Paul.

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